I have a slight brain block while pondering miller cycle engines. Just to clarify- the specific type i’m referring to is like a forced induction version of the atkinson cycle.

So my thought is this- I know the atkinson cycle engine gains efficicancy by allowing some intake charge to escape(therefore increasing the expansion ratio),and that the miller variant makes up for the inherent power losses by adding forced induction. But why is a miller engine more efficient than any normal ICE?
The Miller uses forced induction but lets some of that intake charge back out again.... which doesnt sound much different to the end result a normal engine does! So where is the advantage?